"bottom of a sleeve," mid-14c., cuffe "hand covering, mitten, glove," perhaps somehow from Medieval Latin cuffia "head covering," of uncertain origin. Sense of "band around the sleeve" is first attested 1520s; sense of "hem of trousers" is 1911. Off the cuff "extemporaneously" is 1938 American English colloquial, suggesting an actor or speaker reading from notes jotted on his shirt sleeves rather than learned lines. Cuff links is from 1897.